Find distance from center of equilateral triangle to edge in given angle

Question

I need to find the distance from the barycenter of an equilateral triangle to the edge in a given angle.

Here's a little sketch:

Given the outer radius of the triangle, the angle and the rotation (assuming the rotation in the picture would be $0$), I need to find the distance from the point on the edge (marked as red in the sketch) to the center.

Any help is appreciated!

Answer 1

This expression works for your particular choice of the angle: $$d=\frac{R}{2\cos(\arccos(\sin(3\alpha))/3)},$$ where $R$ is the radius of circumscribed circle (I assume this was meant by "outer radius of the triangle").